1. Field of the Invention
The present invention relates in general to methods for analyzing jetting bubbles generated by ship, and relates in particular to a method for analyzing effects of micro-bubbles on reducing skin-friction of ships.
2.Description of the Related Art
One of the known methods for reducing the skin-friction phenomenon on ships is a micro-bubble technique. Many bubbly flow models can perform computations of various properties of flow fields only if void fraction distributions are already known. Therefore, it is crucial to clarify the mechanism of void fraction distribution in bubbly flow in order to achieve accurate estimation of friction reduction effects. Furthermore, when it is desired to apply such a micro-bubble technique for friction reduction in actual situations, it becomes necessary, for design purposes, to estimate a void fraction which would be produced in a given bubbly flow field by varying the bubble supply rates during various computational processes. Therefore, from a viewpoint of practical applications also, knowledge of void fraction distribution in a bubbly flow is important for developing an analytical methodology.
For example, Guin et al. presented precision experiments involving bubbly flows in horizontal channels which demonstrated a close relationship of void fractions in near-wall surfaces to reduction in the skin-friction effects (Report A, "Reduction of skin-friction by micro-bubbles and its relation with near-wall bubble concentration in a channel", JMST, Vol. 1, No.5, pp.241-254, 1996). In their report, it is confirmed that, when the supply air volume flow is increased under a constant flow speed, the location of the peak in void fraction moves away from the wall.
Also, although different than the present study which relates to bubbles within the horizontal channel, there have been a study related to vertically ascending or descending bubbly flows. Sato et al. demonstrated that, while observing bubble behavior of low void fractions (at 5% of the peak value), small bubbles tended to move away from the wall surface at higher velocities (Report B, "A Bubbly flow Study: Report No. 2, Effects of water velocity and flow passage size on bubble behavior", Kiron, 43:2288-0296, 1977).
However, such observations are difficult to explain theoretically, on the basis of the lift force only, presented typically in Report C by Saffman ("The lift on a small sphere in a slow shear flow", JFM22:385-400, 1965). It is evident that conventional theories are not able to resolve the question of how to analytically treat the effect of bubbles on the behavior of a liquid phase in a bubbly flow.
Studies on formulating estimation equations are found, for example, in a Report D by Kataoka ("Modeling and prediction of turbulence in bubbly two-phase flow", 2nd. International Conference on Multi-phase Flow, '95, Japan, pp. M02-11-16, 1995). In this study, the flow volumes were computed from estimation equations based on experimental determination of void fraction distributions. However, a theoretical explanation was not offered for the mechanisms of developing void fraction distribution, and it remained as a topic to be resolved.
The present authors demonstrated a simple Lagrangian formulation from practical viewpoints (Report E, "Simple Lagrangian formulation of bubbly flow in a turbulent boundary layer, or bubbly boundary layer flow", JMST, Vol. 2, No. 1, pp. 1-11, 1997). In this study, a model for explaining the skin-friction reduction was presented involving a macroscopic expression for the effects of bubbles on turbulence in the liquid phase that assumed an average void fraction within a boundary layer.